Finite Group Databasebeta

← C2×D11×#407 #15617201

Subgroups — C2×D11×#407 #15617201

Order 2816.

7214 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D11C211yesmaximal, characteristic
2C22×M16×D11C212yesmaximal, complemented
3C2×#10622820C211yesmaximal, characteristic, complemented
4C2×#10622739C212yesmaximal, complemented
5C2×#10622339C214yesmaximal, complemented
6D11×#407C2116yesmaximal, direct product factor
7C2×D11×C22⋊C8C214yesmaximal, complemented
8C2×C11×#407C211yesmaximal, characteristic, complemented
9C25×D11C411yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×Dic11C411yescharacteristic
12C23×C4×D11—216no—
13C23×C4×D11C411yescharacteristic
14C23×C4×D11C411yescharacteristic
15C23×C4×D11C418yes—
16C23×C4×D11C412yes—
17C23×C4×D11C412yes—
18C23×C4×D11C2212yes—
19C23×C4×D11C2218yes—
20C23×C4×D11C2212yes—
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×M16C2212yescomplemented
24C22×#4318C2212yescomplemented
25C2×M16×D11—216no—
26C2×M16×D11C22116yescomplemented
27C22×#4313C2214yescomplemented
28C22×C8×D11C2214yescomplemented
29C11×#407C2218yescomplemented
30C2×C11×C22⋊C8C2214yescomplemented
31#10622820C2218yescomplemented
32C2×C22⋊(C11⋊C8)C2214yescomplemented
33#10622739C22116yescomplemented
34C2×(C2×D11)⋊C8C2218yescomplemented
35#10622339C22132yescomplemented
36D11×C22⋊C8C22132yescomplemented
37C25×C11C2×C411yescharacteristic
38C24×D11—28no—
39C24×D11—216no—
40C24×D11C2×C411yescharacteristic
41C24×D11C2×C412yes—
42C24×D11C2×C418yes—
43C24×D11C2×C411yescharacteristic
44C24×D11C2×C412yes—
45C23×C4×C11—28no—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2×C412yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2314yes—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—28no—
53C23×Dic11C2×C418yes—
54C23×Dic11C2×C412yes—
55C23×Dic11C2×C412yes—
56C23×Dic11C2×C411yescharacteristic
57C23×Dic11C2×C411yescharacteristic
58C22×C4×D11—28no—
59C22×C4×D11—28no—
60C22×C4×D11—28no—
61C22×C4×D11—264no—
62C22×C4×D11—216no—
63C22×C4×D11—216no—
64C22×C4×D11—216no—
65C22×C4×D11—216no—
66C22×C4×D11—264no—
67C22×C4×D11C2×C418yes—
68C22×C4×D11C2×C412yes—
69C22×C4×D11C2×C412yes—
70C22×C4×D11C2×C4116yes—
71C22×C4×D11C2×C418yes—
72C22×C4×D11C2×C418yes—
73C22×C4×D11C2×C4116yes—
74C22×C4×D11C2×C418yes—
75C22×C4×D11C2×C412yes—
76C22×C4×D11C2×C412yes—
77C22×C4×D11C2×C414yes—
78C22×C4×D11C2×C412yes—
79C22×C4×D11C2×C414yes—
80C22×C4×D11C2×C411yescharacteristic
81C22×C4×D11C2×C411yescharacteristic
82C22×C4×D11D4116yes—
83C22×C4×D11C2312yes—
84C22×C4×D11C2314yes—
85C22×C4×D11C2318yes—
86C22×C4×D11C2318yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2314yes—
90C2×C11×M16—28no—
91C2×C11×M16C2318yescomplemented
92C22×C8×C11C2314yescomplemented
93C2×#4318—28no—
94C2×#4318C2318yescomplemented
95C22×C11⋊C8C2314yescomplemented
96M16×D11—264no—
97C2×#4313—216no—
98C2×#4313C23116yescomplemented
99C2×C8×D11—216no—
100C2×C8×D11C23116yescomplemented
101C11×C22⋊C8C23116yescomplemented
102C22⋊(C11⋊C8)C23116yescomplemented
103(C2×D11)⋊C8C23132yescomplemented
104C22×#407—111nomaximal, Sylow
105C24×C11—24no—
106C24×C11—28no—
107C24×C11C22×C414yes—
108C24×C11C22×C411yescharacteristic
109C24×C11C22×C412yes—
110C23×D11—2128no—
111C23×D11—24no—
112C23×D11—28no—
113C23×D11—28no—
114C23×D11—232no—
115C23×D11—28no—
116C23×D11—28no—
117C23×D11—28no—
118C23×D11—28no—
119C23×D11—28no—
120C23×D11—264no—
121C23×D11C22⋊C418yes—
122C23×D11M16116yescomplemented
123C23×D11C22×C414yes—
124C23×D11C22×C418yes—
125C23×D11C22×C411yescharacteristic
126C23×D11C22×C414yes—
127C23×D11C22×C412yes—
128C23×D11C22×C418yes—
129C23×D11C22×C411yescharacteristic
130C22×C4×C11—24no—
131C22×C4×C11—216no—
132C22×C4×C11—28no—
133C22×C4×C11—28no—
134C22×C4×C11—216no—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C22×C418yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D418yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—232no—
146C22×Dic11—28no—
147C22×Dic11—28no—
148C22×Dic11—24no—
149C22×Dic11C22⋊C418yes—
150C22×Dic11C22×C414yes—
151C22×Dic11C22×C418yes—
152C22×Dic11C22×C418yes—
153C22×Dic11C22×C412yes—
154C22×Dic11C22×C414yes—
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C2×C4×D11—232no—
158C2×C4×D11—28no—
159C2×C4×D11—28no—
160C2×C4×D11—232no—
161C2×C4×D11—264no—
162C2×C4×D11—232no—
163C2×C4×D11—264no—
164C2×C4×D11—232no—
165C2×C4×D11—232no—
166C2×C4×D11—232no—
167C2×C4×D11—28no—
168C2×C4×D11—28no—
169C2×C4×D11—216no—
170C2×C4×D11—28no—
171C2×C4×D11—28no—
172C2×C4×D11—216no—
173C2×C4×D11C22⋊C4132yes—
174C2×C4×D11C22⋊C418yes—
175C2×C4×D11C22⋊C418yes—
176C2×C4×D11C22×C418yes—
177C2×C4×D11C22×C418yes—
178C2×C4×D11C22×C418yes—
179C2×C4×D11C22×C418yes—
180C2×C4×D11C22×C414yes—
181C2×C4×D11C22×C418yes—
182C2×C4×D11C22×C412yes—
183C2×C4×D11C22×C414yes—
184C2×C4×D11C22×C412yes—
185C2×C4×D11C22×C414yes—
186C2×C4×D11C2×D418yes—
187C2×C4×D11C2×D418yes—
188C2×C4×D11C2×D4132yes—
189C2×C4×D11C2414yes—
190C2×C4×D11C2412yes—
191C2×C4×D11C2412yes—
192C11×M16—216no—
193C2×C8×C11—28no—
194C2×C8×C11C2418yescomplemented
195#4318—216no—
196C2×C11⋊C8—28no—
197C2×C11⋊C8C2418yescomplemented
198#4313—232no—
199C8×D11—232no—
200C25×C4—111no—
201C23×M16—112no—
202C2×#407—1116no—
203C2×#407—114no—
204C2×#407—111no—
205C2×#407—112no—
206C2×#407D1111yescharacteristic, direct product factor
207C22×C22⋊C8—114no—
208C23×C11—232no—
209C23×C11—28no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—216no—
214C23×C11C2×C22⋊C414yes—
215C23×C11C2×M1618yescomplemented
216C23×C11C23×C412yes—
217C23×C11C23×C414yes—
218C23×C11C23×C411yescharacteristic
219C22×D11—264no—
220C22×D11—232no—
221C22×D11—2256no—
222C22×D11—28no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—216no—
227C22×D11—216no—
228C22×D11—216no—
229C22×D11—216no—
230C22×D11—216no—
231C22×D11—216no—
232C22×D11—216no—
233C22×D11—232no—
234C22×D11—264no—
235C22×D11C2×C22⋊C414yes—
236C22×D11C2×C22⋊C4116yes—
237C22×D11C2×C22⋊C414yes—
238C22×D11C2×M1618yes—
239C22×D11C2×M16132yescomplemented
240C22×D11C2×M1618yescomplemented
241C22×D11C23×C412yes—
242C22×D11C23×C414yes—
243C22×D11C23×C412yes—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—28no—
247C2×C4×C11—216no—
248C2×C4×C11—28no—
249C2×C4×C11C2×C22⋊C418yes—
250C2×C4×C11C2×C22⋊C414yes—
251C2×C4×C11C23×C414yes—
252C2×C4×C11C23×C412yes—
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D414yes—
255C2×C4×C11C22×D418yes—
256C2×C4×C11C2511yescharacteristic
257C2×Dic11—28no—
258C2×Dic11—24no—
259C2×Dic11—216no—
260C2×Dic11—216no—
261C2×Dic11C2×C22⋊C4116yes—
262C2×Dic11C2×C22⋊C414yes—
263C2×Dic11C2×C22⋊C414yes—
264C2×Dic11C23×C414yes—
265C2×Dic11C23×C412yes—
266C2×Dic11C23×C412yes—
267C4×D11—216no—
268C4×D11—216no—
269C4×D11—28no—
270C4×D11—216no—
271C4×D11—28no—
272C4×D11—216no—
273C4×D11—216no—
274C4×D11C2×C22⋊C418yes—
275C4×D11C2×C22⋊C4116yes—
276C4×D11C2×C22⋊C418yes—
277C4×D11C2×C22⋊C4116yes—
278C4×D11C22×D418yes—
279C4×D11C22×D418yes—
280C8×C11—28no—
281C11⋊C8—28no—
282C26—111no—
283C24×C4—111no—
284C24×C4—111no—
285C24×C4—112no—
286C24×C4—118no—
287C24×C4—112no—
288C24×C4—111no—
289C24×C4—111no—
290C24×C4—112no—
291C24×C4—118no—
292C24×C4—112no—
293C24×C4—111no—
294C24×C4—2216no—
295C24×C4C2×D1111yescharacteristic
296C22×M16—112no—
297C22×M16—1116no—
298C22×M16—114no—
299C22×M16—2216no—
300C22×M16C2×D1112yescomplemented
301C23×C8—114no—
302#407—118no—
303#407—1116no—
304#407—1132no—
305#407C2×D1118yesdirect product factor
306C2×C22⋊C8—114no—
307C2×C22⋊C8—118no—
308C2×C22⋊C8—1132no—
309C2×C22⋊C8C2×D1114yescomplemented
310C22×C11—232no—
311C22×C11—28no—
312C22×C11—216no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11C22×C22⋊C414yes—
317C22×C11C22×C22⋊C412yes—
318C22×C11C22×M1614yes—
319C22×C11C22×M1618yescomplemented
320C22×C11C24×C411yescharacteristic
321C2×D11—264no—
322C2×D11—232no—
323C2×D11—28no—
324C2×D11—216no—
325C2×D11—24no—
326C2×D11—24no—
327C2×D11—24no—
328C2×D11—232no—
329C2×D11—264no—
330C2×D11#407116yesdirect product factor
331C2×D11C22×C22⋊C414yes—
332C2×D11C22×C22⋊C414yes—
333C2×D11C22×M1618yes—
334C2×D11C22×M1618yescomplemented
335C4×C11—24no—
336C4×C11C22×C22⋊C412yes—
337C4×C11C22×C22⋊C414yes—
338C4×C11C23×D412yes—
339Dic11—24no—
340Dic11C22×C22⋊C414yes—
341Dic11C22×C22⋊C414yes—
342C25—111no—
343C25—112no—
344C25—118no—
345C25—112no—
346C25—111no—
347C25—228no—
348C25—2216no—
349C25C4×D1111yescharacteristic
350C23×C4—28no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—114no—
354C23×C4—111no—
355C23×C4—1116no—
356C23×C4—114no—
357C23×C4—111no—
358C23×C4—111no—
359C23×C4—118no—
360C23×C4—112no—
361C23×C4—112no—
362C23×C4—111no—
363C23×C4—112no—
364C23×C4—112no—
365C23×C4—118no—
366C23×C4—118no—
367C23×C4—1116no—
368C23×C4—1116no—
369C23×C4—118no—
370C23×C4—112no—
371C23×C4—118no—
372C23×C4—112no—
373C23×C4—112no—
374C23×C4—114no—
375C23×C4—118no—
376C23×C4—118no—
377C23×C4—114no—
378C23×C4—112no—
379C23×C4—228no—
380C23×C4—2216no—
381C23×C4—2264no—
382C23×C4—2216no—
383C23×C4—2216no—
384C23×C4—2216no—
385C23×C4—2264no—
386C23×C4—228no—
387C23×C4—228no—
388C23×C4—228no—
389C23×C4C4×D1111yescharacteristic
390C23×C4C4×D1114yes—
391C23×C4C4×D1112yes—
392C23×C4C22×D1114yes—
393C23×C4C22×D1112yes—
394C23×C4C22×D1111yescharacteristic
395C2×M16—28no—
396C2×M16—118no—
397C2×M16—1116no—
398C2×M16—2216no—
399C2×M16—2264no—
400C2×M16—228no—
401C2×M16C22×D1118yescomplemented
402C22×C8—114no—
403C22×C8—1116no—
404C22×C8—2216no—
405C22×C8C22×D1114yescomplemented
406C22⋊C8—1116no—
407C22⋊C8—1132no—
408C22⋊C8C22×D11116yescomplemented
409C2×C11—24no—
410C2×C11—28no—
411C2×C11C2×#40714yescomplemented
412C2×C11C23×C22⋊C411yescharacteristic
413C2×C11C23×M1612yes—
414D11—24no—
415D11—28no—
416D11C2×#40718yesdirect product factor
417C24—24no—
418C24—28no—
419C24—111no—
420C24—118no—
421C24—1116no—
422C24—114no—
423C24—118no—
424C24—111no—
425C24—112no—
426C24—118no—
427C24—114no—
428C24—228no—
429C24—2232no—
430C24—228no—
431C24—228no—
432C24—228no—
433C24—228no—
434C24—228no—
435C24—2264no—
436C24—22128no—
437C24—224no—
438C24—228no—
439C24C2×C4×D1114yes—
440C24C2×C4×D1111yescharacteristic
441C24C2×C4×D1112yes—
442C22×C4—24no—
443C22×C4—216no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—216no—
447C22×C4—118no—
448C22×C4—114no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—118no—
452C22×C4—1132no—
453C22×C4—118no—
454C22×C4—114no—
455C22×C4—114no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—118no—
459C22×C4—1132no—
460C22×C4—118no—
461C22×C4—112no—
462C22×C4—112no—
463C22×C4—118no—
464C22×C4—118no—
465C22×C4—114no—
466C22×C4—112no—
467C22×C4—118no—
468C22×C4—118no—
469C22×C4—118no—
470C22×C4—118no—
471C22×C4—118no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—2232no—
475C22×C4—228no—
476C22×C4—228no—
477C22×C4—2232no—
478C22×C4—2264no—
479C22×C4—2264no—
480C22×C4—2232no—
481C22×C4—2232no—
482C22×C4—2232no—
483C22×C4—228no—
484C22×C4—2232no—
485C22×C4—228no—
486C22×C4—2232no—
487C22×C4—228no—
488C22×C4—228no—
489C22×C4—224no—
490C22×C4—2216no—
491C22×C4—228no—
492C22×C4—228no—
493C22×C4—2216no—
494C22×C4C2×C4×D1114yes—
495C22×C4C2×C4×D1112yes—
496C22×C4C2×C4×D1118yes—
497C22×C4C2×C4×D1114yes—
498C22×C4C2×C4×D1111yescharacteristic
499C22×C4C2×C4×D1112yes—
500C22×C4D4×D1118yes—
501C22×C4C23×D1114yes—
502C22×C4C23×D1112yes—
503C22×C4C23×D1111yescharacteristic
504M16—216no—
505M16—2232no—
506M16—2216no—
507C2×C8—28no—
508C2×C8—118no—
509C2×C8—2232no—
510C2×C8—228no—
511C2×C8C23×D1118yescomplemented
512C11C22×#40711yescharacteristic, complemented, Sylow
513C23—232no—
514C23—28no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—216no—
519C23—114no—
520C23—118no—
521C23—112no—
522C23—1116no—
523C23—114no—
524C23—118no—
525C23—1132no—
526C23—112no—
527C23—114no—
528C23—2216no—
529C23—2216no—
530C23—2232no—
531C23—2264no—
532C23—2216no—
533C23—2216no—
534C23—2216no—
535C23—2216no—
536C23—22256no—
537C23—2232no—
538C23—2264no—
539C23—228no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—2216no—
544C23C22⋊C4×D1114yes—
545C23M16×D1118yescomplemented
546C23C22×C4×D1112yes—
547C23C22×C4×D1114yes—
548C23C22×C4×D1111yescharacteristic
549C2×C4—28no—
550C2×C4—24no—
551C2×C4—216no—
552C2×C4—28no—
553C2×C4—28no—
554C2×C4—1116no—
555C2×C4—114no—
556C2×C4—114no—
557C2×C4—112no—
558C2×C4—112no—
559C2×C4—118no—
560C2×C4—1116no—
561C2×C4—1116no—
562C2×C4—118no—
563C2×C4—118no—
564C2×C4—118no—
565C2×C4—114no—
566C2×C4—2216no—
567C2×C4—2216no—
568C2×C4—2216no—
569C2×C4—2216no—
570C2×C4—2216no—
571C2×C4—2216no—
572C2×C4—228no—
573C2×C4—224no—
574C2×C4—2216no—
575C2×C4—228no—
576C2×C4—228no—
577C2×C4C22⋊C4×D1118yes—
578C2×C4C22⋊C4×D1114yes—
579C2×C4C22×C4×D1114yes—
580C2×C4C22×C4×D1112yes—
581C2×C4C22×C4×D1111yescharacteristic
582C2×C4C2×D4×D1114yes—
583C2×C4C2×D4×D1118yes—
584C2×C4C24×D1111yescharacteristic
585C8—28no—
586C8—228no—
587C22—232no—
588C22—28no—
589C22—216no—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—1116no—
594C22—114no—
595C22—118no—
596C22—114no—
597C22—118no—
598C22—2232no—
599C22—2264no—
600C22—2232no—
601C22—2264no—
602C22—228no—
603C22—2216no—
604C22—224no—
605C22—224no—
606C22—224no—
607C22C2×C22⋊C4×D1114yes—
608C22C2×C22⋊C4×D1112yes—
609C22C2×M16×D1114yes—
610C22C2×M16×D1118yescomplemented
611C22C23×C4×D1111yescharacteristic
612C4—24no—
613C4—114no—
614C4—114no—
615C4—224no—
616C4C2×C22⋊C4×D1114yes—
617C4C2×C22⋊C4×D1112yes—
618C4C22×D4×D1112yes—
619C2—24no—
620C2—28no—
621C2—118no—
622C2—224no—
623C2—228no—
624C2D11×#40714yesdirect product factor
625C2C22×C22⋊C4×D1111yescharacteristic
626C2C22×M16×D1112yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#407C2
socleC23×C11C23×C4
prime radicalC25×D11C4
cosocleC2×C4×C11C25
hypercenterC2×#407D11
hypocenterC11C22×#407
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×M16×D11C2semidirect
3. C2×#10622820C2semidirect
4. C2×#10622739C2semidirect
5. C2×#10622339C2semidirect
6. D11×#407C2direct (N × H)
7. C2×D11×C22⋊C8C2semidirect
8. C2×C11×#407C2semidirect
23. C22×C11×M16C22semidirect
24. C22×#4318C22semidirect
26. C2×M16×D11C22semidirect
27. C22×#4313C22semidirect
28. C22×C8×D11C22semidirect
29. C11×#407C22semidirect
30. C2×C11×C22⋊C8C22semidirect
31. #10622820C22semidirect
32. C2×C22⋊(C11⋊C8)C22semidirect
33. #10622739C22semidirect
34. C2×(C2×D11)⋊C8C22semidirect
35. #10622339C22semidirect
36. D11×C22⋊C8C22semidirect
91. C2×C11×M16C23semidirect
92. C22×C8×C11C23semidirect
94. C2×#4318C23semidirect
95. C22×C11⋊C8C23semidirect
98. C2×#4313C23semidirect
100. C2×C8×D11C23semidirect
101. C11×C22⋊C8C23semidirect
102. C22⋊(C11⋊C8)C23semidirect
103. (C2×D11)⋊C8C23semidirect
122. C23×D11M16semidirect
194. C2×C8×C11C24semidirect
197. C2×C11⋊C8C24semidirect
206. C2×#407D11direct (N × H)
215. C23×C11C2×M16semidirect
239. C22×D11C2×M16semidirect
240. C22×D11C2×M16semidirect
300. C22×M16C2×D11semidirect
305. #407C2×D11direct (N × H)
309. C2×C22⋊C8C2×D11semidirect
319. C22×C11C22×M16semidirect
330. C2×D11#407direct (N × H)
334. C2×D11C22×M16semidirect
401. C2×M16C22×D11semidirect
405. C22×C8C22×D11semidirect
408. C22⋊C8C22×D11semidirect
411. C2×C11C2×#407semidirect
416. D11C2×#407direct (N × H)
511. C2×C8C23×D11semidirect
512. C11C22×#407semidirect
545. C23M16×D11semidirect
610. C22C2×M16×D11semidirect
624. C2D11×#407direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C24×C4×D112
C22×M16×D112
C2×#106228202
C2×#106227392
C2×#106223392
D11×#4072
C2×D11×C22⋊C82
C2×C11×#4072
C22×#40711